Warm Up

2. Warm Up Five different books are on a shelf. In how many different ways could you arrange them? 2) How many ways can gold, silver, and bronze medals be awarded for a race run by 8 people? Solution #1 The five books can be arranged in 5 · 4 · 3 · 2 · 1 = 5! = 120 ways. Solution#2: Using the permuation formula we find P(8, 3) = 8!(8−3)! = 336 ways of them is r the second letter?

3. What is the expected value of winning it cost one dollar to win and if you win you get $35? expected value is: −1×37⁄38 + 35×1⁄38 = −0.0526

4. Probability model to find expected value and standard deviation  mathematical representation of a random phenomenon. It is defined by its sample spaceandprobabilities associated with each event A probability assigned for each possible outcome All probabilities add up to 1

5. A life insurance company charge $50 per year, they want to find out if they will have losses. They have 1000 policy holders who get:$10,000 if die: 1 expected a year$5,000 if disabled: 2 expected a year$0: if nothing happens How to find out about losses: Set up probability model table Find expected value Find standard deviation

6. Standard Deviation for Probability Model X = each outcome P(x) = probability of each outcome #1: find: outcome – expected value #2: Square the answer for each outcome: #3: multiply each answer by p(x): #4: Add them all up: #5: square root the sum